The detection of faint sources is a key step in several areas of signal and image processing. The reliability of the detection depends on two key components: (i) the detection criterion used to derive detection maps in which the signature of a source takes the form of a detection peak, and (ii) the extraction procedure identifying the meaningful detections. In this work, the expected false discovery rate guides the selection of meaningful detections. A procedure is designed to account for correlations in the detection maps. This prevents the issue of the multiple detections of a single source and corrects the number of effective independent tests performed. The proposed approach is evaluated on an astrophysical application: the detection of exoplanets by high-contrast imaging.